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Finite dimensional approximations for Nica-Pimsner algebrasApr 22 2019We give necessary and sufficient conditions for nuclearity of Cuntz-Nica-Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping stone to tackle product systems over quasi-lattices ... More Invariant measures for Cantor dynamical systemsApr 21 2019This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure or finitely ... More Positivity of $2\times 2$ block matrices of operatorsApr 18 2019We review some of the significant generalizations and applications of the celebrated Douglas theorem on the equivalence of factorization, range inclusion, and majorization of operators. We then apply it to find a characterization of the positivity of ... More Extensions of the vector-valued Hausdorff-Young inequalitiesApr 16 2019In this paper we study the vector-valued analogues of several inequalities for the Fourier transform. In particular, we consider the inequalities of Hausdorff--Young, Hardy--Littlewood, Paley, Pitt, Bochkarev and Zygmund. The Pitt inequalities include ... More Sylvester equations and polynomial separation of spectraApr 16 2019Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of $p(A)$ and $p(B)$ ... Moremath.FA15A24, 47A10, 47A60, 47A62, 65F08, 65F10, 65J10 15A24, 47A10, 47A60,
47A62, 65F08, 65F10, 65J10 15A24 47A10 47A60 47A62 65F08 65F10 65J10 Embeddings of uniform Roe algebrasApr 15 2019In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces $X$ and $Y$, we are interested in which large scale geometric properties are stable under embedding of the uniform Roe algebra of $X$ into the uniform ... More Isomorphism in WaveletsApr 15 2019Two scaling functions $\varphi_A$ and $\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\varphi_A \simeq \varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be $d\times d$ ... More Structure and $K$-theory of $\ell^p$ uniform Roe algebrasApr 15 2019In this paper, we characterize when the $\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\in [1,\infty)$. Moreover, we show that the $\ell^p$ uniform Roe algebra ... More II$_1$ factors with exotic central sequence algebrasApr 15 2019We provide a class of separable II$_1$ factors $M$ whose central sequence algebra is not the "tail" algebra associated to any decreasing sequence of von Neumann subalgebras of $M$. This settles a question of McDuff \cite{Mc69d}. Prime II$_1$ factors arising from actions of product groupsApr 14 2019We prove that any II$_1$ factor arising from a free ergodic probability measure preserving action $\Gamma\curvearrowright X$ of a product $\Gamma=\Gamma_1\times\dots\times\Gamma_n$ of icc hyperbolic, free product or wreath product groups is prime, provided ... More Noncommutative Orlicz sequence spaces and some applicationsIApr 13 2019In this paper, the definition of noncommutative Orlicz sequence spaces is given, these spaces generalize the Schatten classes Sp(H). After some relations of trace and norm on this spaces have been researched, one give the criterion of reflexivity of these ... More Interpolation of compact bilinear operatorsApr 13 2019We investigate the stability of compactness of bilinear operators acting on the product of interpolation of Banach spaces. We develop a general framework for such results and our method applies to abstract methods of interpolation in the senseof Aronszajn ... More Approximation in the mean by rational functionsApr 12 2019Apr 19 2019For $1\le t < \infty$, a compact subset $K\subset\mathbb C$, and a finite positive measure $\mu$ supported on $K$, $R^t(K, \mu)$ denotes the closure in $L^t(\mu)$ of rational functions with poles off $K$. Let $\text{abpe}(R^t(K, \mu))$ denote the set ... More Approximation in the mean by rational functionsApr 12 2019For $1\le t < \infty$, a compact subset $K$ of the complex plane $\mathbb C$, and a finite positive Borel measure $\mu$ supported on $K$, $R^t(K, \mu)$ denotes the closure in $L^t(\mu)$ of the rational functions with poles off $K$. Let $\text{abpe}(R^t(K, ... More On the linearity of order-isomorphismsApr 12 2019A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of its engaged ... More Some Convergence Theorems for Operator SequencesApr 11 2019Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and $\left\{ \frac{1}{n}\sum_{i=0}^{n-1}A^{i}TB^{i}% ... More Tight Bounds for the Subspace Sketch Problem with ApplicationsApr 11 2019In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$, with probability ... More Generalized-lush spaces revisitedApr 10 2019We study geometric properties of GL-spaces. We demonstrate that every finite-dimensional GL-space is polyhedral; that in dimension 2 there are only two, up to isometry, GL-spaces, namely the space whose unit sphere is a square (like $\ell_\infty^2$ or ... More On Matrix Rearrangement InequalitiesApr 10 2019Given two symmetric and positive semidefinite square matrices $A, B$, is it true that any matrix given as the product of $m$ copies of $A$ and $n$ copies of $B$ in a particular sequence must be dominated in the spectral norm by the ordered matrix product ... More Characterizations of derivationsApr 10 2019The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations. In Chapter 2 ... More Approximation in $L^p(μ)$ with deep ReLU neural networksApr 09 2019We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $\varrho(x) = \max\{0,x\}$ by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two categories: ... More Martingale Optimal Transport DualityApr 09 2019We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional constraints ... More On distributional adjugate and derivative of the inverseApr 09 2019Let $\Omega\subset\er^3$ be a domain and let $f\in BV_{\loc}(\Omega,\er^3)$ be a homeomorphism such that its distributional adjugate $\Adj Df$ is a finite Radon measure. Very recently in \cite{HKL} it was shown that its inverse has bounded variation $f^{-1}\in ... More A summability principle and applicationsApr 09 2019The main result of the present paper is a new Inclusion Theorem for summing operators, that encompasses several recent similar results as particular cases. As applications, we improve estimates of certain Hardy--Littlewood inequalities for multilinear ... More Plans on measures and AM-modulusApr 09 2019For measuring families of curves, or, more generally, of measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper [4], Ambrosio, Di Marino and Savar\'e proved that these two approaches ... More On Riemann Integration in Metrizable Vector SpacesApr 09 2019In classical analysis, Lebesgue first proved that $\mathbb{R}$ has the property that each Riemann integrable function from $[a,b]$ into $\mathbb{R}$ is continuous almost everywhere. This property is named as the Lebesgue property. Though the Lebesgue ... More A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spacesApr 09 2019We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as "the" Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral ... Moremath.FAmath.NAmath.OCmath.PRPrimary 47L60, 46N30, 46N50, 42C15, 65R10, 05C50, 05C75, 31C20,
60J20, 26E40, 65D15, 41A65, Secondary 46N20, 22E70, 31A15, 58J65, 81S25,
68T05 On complex symmetric block Toeplitz operatorsApr 09 2019In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy space $H_{{\mathbb ... More Clark measures on the complex sphereApr 08 2019Let $B_d$ denote the unit ball of $\mathbb{C}^d$, $d\ge 1$. Given a holomorphic function $\varphi: B_d \to B_1$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\partial B_1$, of Clark measures on the unit sphere $\partial B_d$. ... Moremath.CVmath.FA32A35, 30E20, 30J05, 31C10, 32A26, 32A40, 43A85, 46E27, 46J15,
47A45, 47B33 Unilateral weighted shifts on $\ell^2$Apr 08 2019Given a unilateral shift $B_w$ (determined by a bounded sequence $w$), a sequence $x \in \ell^2$ is "hypercyclic" for $w$ iff the forward iterates of $x$ under $B_w$ are dense in $\ell^2$. We show that it is possible to make the set of $x \in \ell^2$ ... More Tracial moment problems on hypercubesApr 07 2019In this paper we study the tracial moment problem on the hypercube $[-1,1]^n$. We propose the concept "sequential tracial $K$-moment problem" for sequences of scalar matrices and establish a sufficient condition for the solvability of the sequential tracial ... More Tracial moment problems on hypercubesApr 07 2019Apr 09 2019In this paper we introduce the "tracial $K$-moment problem" and the "sequential matrix-valued $K$-moment problem" and show the equivalence of the solvability of these problems. Using a Haviland's theorem for matrix polynomials, we solve these $K$-moment ... More Low-Rank Approximability and Entropy Area Laws for PDEsApr 06 2019We show how local interactions in a partial differential equation (PDE) model lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the ... More Low-Rank Approximability and Entropy Area Laws for PDEsApr 06 2019Apr 11 2019We show how local interactions in a partial differential equation (PDE) model lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the ... More An improvement on the relatively compactness criteriaApr 06 2019This paper is devoted to the study of the relatively compact sets in Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function ... More Spectral analysis of matrix scaling and operator scalingApr 05 2019We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent algorithm also has ... More Elliptic problems and holomorphic functions in Banach spacesApr 05 2019In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that $\langle f,x'\rangle$ ... More Continuity of extensions of Lipschitz mapsApr 05 2019We establish the sharp rate of continuity of extensions of $\mathbb{R}^m$-valued $1$-Lipschitz maps from a subset $A$ of $\mathbb{R}^n$ to a $1$-Lipschitz maps on $\mathbb{R}^n$. We consider several cases when there exists an extension with preserved ... More On generalized Hölder's inequality in weak Morrey SpacesApr 05 2019In this note we reprove generalized H\"{o}lder's inequality in weak Morrey spaces. In particular, we get sharper bounds than those in \cite{gunawan2}. The bounds are obtained through the relation of weak Morrey spaces and weak Lebesgue spaces. Kato S-spectrum in the quaternionic settingApr 05 2019In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the S-spectrum and it contains ... More A bridge between quaternionic and complex numerical rangesApr 04 2019We obtain a sufficient condition for the convexity of quaternionic numerical range for complex matrices in terms of its complex numerical range. It is also shown that the Bild coincides with complex numerical range for real matrices. From this result ... More Controlled $g$-frames in Hilbert $C^*$-modulesApr 04 2019To improve the numerical efficiency of iterative algorithms for inverting the frame operator, the controlled frame was introduced, and has been given more importance. In this paper, we introduce the concept of controlled g-frames in Hilbert $C^{*}$-modules. ... More Controlled $g$-frames in Hilbert $C^*$-modulesApr 04 2019Apr 12 2019To improve the numerical efficiency of iterative algorithms for inverting the frame operator, the controlled frame was introduced by Balazs et al. \cite{Balazs}, and has since been given more importance. In this paper, we introduce the concept of controlled ... More Thick Families of Geodesics and DifferentiationApr 04 2019The differentiation theory of Lipschitz functions taking values in a Banach space with the Radon-Nikod\'ym property (RNP), originally developed by Cheeger-Kleiner, has proven to be a powerful tool to prove non-biLipschitz embeddability of metric spaces ... More Sets of $p$-restriction and $p$-spectral synthesisApr 04 2019In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set $E$ in $\mathbb{R}^n$ to have the $p$-restriction property. We also extend the concept of spectral synthesis to $L^p(\mathbb{R}^n)$ ... More Self-adjointness of perturbed bi-Laplacians on infinite graphsApr 03 2019We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result ... More Norm Inequalities for Inner Product Type Integral TransformersApr 03 2019In this paper, we give a detailed survey on norm inequalities for inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral ... More On The Development of Nonlinear Operator TheoryApr 03 2019The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can fall in some ... More